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Landfill Gas Pressure Relief Layer  -Design Calculator

Problem Statement

Landfill gas (LFG) pressure underneath a lined cover system can significantly reduce the effective normal stress on the liner, which can affect cover soil stability.The Landfill Gas Stability Calculator can be used to verify the factor of safety of a landfill cover subject to landfill gas pressure underneath a geomembrane liner.

Large-scale landfill cover slope failures have been recorded over the past decade to be directly attributed by an inadequate LFG venting layer.  According to recent studies, based on intrinsic permeability theory into gas transmission rates, the rate of LFG transmissivity is ten times lower than the hydraulic transmissivity in any porous media.  In the past, however, this relationship was believed to be inverse, i.e. the air transmissivity was believed to be 100 times greater than the hydraulic transmissivity.  The resulting miscalculations significantly under design the required transmissivity of the LFG venting layer, which in turn may cause landfill cover slope failures.

Landfill Gas Pressure Relief Layer Calculator - Solutions

Estimation of Gas Flux

The mass flux of gas from the surface of a landfill is site specific and varies spacially and temporally in a given landfill. Hence the amount of gas produced from the waste depends on the waste's type, age, temperature , moisture, other avenues of gas extraction or venting, and barometric pressure. For controlled landfills in enhanced decomposition mode values go up to 0.037 standard cubic meters per wet kilogram of waste per year (m3/kg/yr), however for purposes of cover design typically at the end of the cell's life, R.S. Thiel recommends a gas generation rate of 6.24 x 10-3 m3/kg/yr for municipal solid waste landfills in the Northwestern United States

Eq. (1)

ΦLFG

LFG mass flux(m3/s/m2)

rg

Landfill gas generation rate(m3/kg/yr)

Havg waste

Average waste depth(m)
γwaste Unit weight of waste(kN/m3)

Required LFG Relief Layer Transmissivity

The required gas transmissivity for LFG relief layer based on LFG mass flux, maximum LFG pressure, and spacing between strip drains can be calculated as follows.

Eq. (2)

where:

θrequired LFG

Required LFG layer transmissivity (m2/s)

ugmax

Maximum LFG pressure (kPa)

ΦLFG

LFG mass flux(m3/s/m2)
γLFG Unit weight of LFG (kN/m3)

L

Spacing between strip drains (m)
Eq. (3)

θultimate LFG

Ultimate LFG layer transmissivity (m2/s)

FS

Overall factor of safety

RFin

Intrusion Reduction Factor

RFcr

Creep Reduction Factor

RFcc

Chemical Clogging Reduction Factor

RFbc

Biological Clogging Reduction Factor

TSF

Total Serviceability Factor = FS * RFin * RFcr * RFcc * RFbc

Hydraulic Transmissivity vs. LFG Transmissivity

The gas transmissivity can be converted to a hydraulic transmissivity for the same drainage medium. The intrinsic permeability variables for common liquids and gases are listed in Table 1.

Eq. (4)

where:

θH20

Hydraulic transmissivity (m2/s)

θGAS

gas transmissivity (m2/s)

μgas

Dynamic viscosity of gas (N-s/m2)
μH20 Dynamic viscosity of water (N-s/m2)
γGAS Unit weight of gas (kN/m3)

γH20

Unit weight of water (kN/m3)
 

Table 1. - Intrinsic Permeability Variables for Common Fluids and Gases (70oF)

  Density, ρ Unit Weight, γ Dynamic Viscosity, μ  Kinematic Viscosity, υ
  slug/ft3 kg/m3 pcf N/m3 Centipoise lb-s/ft2 N-s/m2 ft2/s m2/s
Water 1.94 1000 62.4 9800 1.01 2.12E-5 1.01E-3 1.09E-5 1.01E-6
Air 2.34E-3 1.2 .0753 11.8 .018 3.78E-7 1.79E-5 1.63E-4 1.48E-5
CO2 3.55E-3 1.83 .114 17.9 .015 3.15E-7 1.50E-5 8.88E-5 8.21E-6
Methane 1.29E-3 .666 .0416 6.54 .011 2.31E-7 1.10E-5 1.79E-4 1.65E-5
LFG(*) 2.53E-3 1.31 .0815 12.8 .0132 2.77E-7 1.32E-5 1.09E-4 1.01E-5

*55% CO2  ,45% CH4


Check for Reynolds Number

The Reynolds number indicates if a flow is laminar or turbulent.Since laminar flow is the basis for the validity of Darcy's law as used in the LFG relief equation above, a calculator is presented.  For sands, the flow is laminar if Re < 10;  For pipes, the flow is laminar if Re < 2000.  The critical Re for one geonet was reported to be about 500 (Richardson and Zhao, 2000).

Eq. (5)

where:

Re

Reynolds number

ρ

Fluid density (kg/m3)

u

Kinematic viscosity (m2/s)
d Characteristic flow dimension (m)
v Fluid velocity (m/s)


Input Values

Estimation of LFG Mass Flux
rg m3/kg/yr
Hwaste m
γwaste N/m3
ΦLFG m3/s/m2 *The user can opt to input data for this value (if known), of leave 0. If left 0, ΦLFG will be calculated from Eq. 1 based on the input above.
Thicknessrelief m *The thickness is needed to calculate Reynold's number
LFG Relief Layer Transmissivity
ugmax kPa
gLFG kN/m3
L m
Reduction Factors and Safety Factor
Surface Systems
RFin 1.0 - 1.2
RFcr 1.1 - 1.4
RFcc 1.0 - 1.2
RFbc 1.2 - 1.5
FS 2.0 - 3.0


References

Richardson, G.N. and Zhao, A., (2000), "Gas Transmission in Geocomposite Systems", Geotechnical Fabrics Report, March, pp. 20-23, 2000.

Thiel, R.S. (1998), "Design Methodology for a Gas Pressure Relief Layer Below a Geomembrane Landfill Cover to Improve Slope Stability", Geosynthetic International, Vol. 5, No. 6 pp. 589-617.


Copyright 2001 Advanced Geotech Systems.  All rights reserved.